Macbeth first thinks about killing King Duncan after the the three witches prophesize that he will one day be king himself. After he hears this, he asks himself why he contemplates "that suggestion / Whose horrid image doth unfix my hair / And make my seated heart knock at my ribs, / Against the use of nature?" The "suggestion" he is tempted by is the idea that he should kill Duncan, which, as he says, is a sinful thought to have, and unnatural, or "Against the use of nature." He subsequently says in act 1, scene 3, that, "If chance will have me king, why chance may crown me, Without my stir." In other words, if it is his fate to be king, then he should simply let fate take its course and does not need to "stir," or help it along. This implies firstly that he was previously thinking about intervening and helping fate along by killing the king, and secondly that he has now decided that he will not kill the king, but let fate unwind as it will.
Macbeth does not find it easy to simply sit back and let fate take its course, without his help. He is, after all, a proud man of action, used to determining his own fate. In act 1, scene 5, he implores the heavens to "hide (its) fires" and "Let not light see (his) black and deep desires." Here then we can see that Macbeth still has strong and "dark desires" to kill the king, but we can also see that he tries to fight against those desires.
Macbeth's subsequent decision to succumb to his "dark desires" and kill the king can be largely credited to his wife. She decides that when King Duncan comes to their home the next day, he will not leave alive. However, in act 1, scene 7, Macbath acknowledges that he has only one reason to kill Duncan, and that is to satisfy his own ambitions. Indeed, he says that he has no motivation, or "spur / To prick the sides of (his) intent, but only / Vaulting ambition, which o'erleaps itself." Realizing this, he tells his wife that they "shall proceed no further in this business," meaning that they will not kill Duncan. Lady Macbeth nonetheless persists and accuses Macbeth of cowardice, asking him if he is going to "live a coward in (his) own esteem," and telling him to "screw (his) courage to the sticking-place." This proves to be all the persuasion Macbeth needs. He decides to kill Duncan after all and tells his wife that he is now "settled" upon that course.
In summary then, Macbeth's decision to kill King Duncan has two main causes. The first is his own "vaulting ambition," which first gives rise to his "dark desires." The second is his determination always to be the courageous man of action, which his wife exploits. His own ambition is the driving force behind the decision, but he needs his wife to give it a nudge in the right direction. In this way, his ambition is like a boulder teetering on the edge of a cliff, and his wife is the force which tips the boulder over the edge and starts the avalanche.